His relationship with Sasuke could change. Sasuke might be more suspicious of Naruto. Since Aizen was known for his duplicity, Sasuke could think Naruto is hiding something big from him. Their rivalry could take on a different tone, more of a distrust - filled one.
Naruto's friends in Konoha would be very confused. They are used to Naruto's positive and straightforward nature. If he starts acting like an Aizen fan, they might think he has been influenced by something bad. For example, Sakura might try to talk to him and figure out what's wrong, but Naruto could be more secretive, causing strain in their friendship. And with his teachers like Kakashi, they might be worried about this new direction Naruto is taking.
He could also become more cautious. If his dad is into Aizen's ways, Naruto might be more aware of the potential for deception and hidden motives in others. This could make him a more astute ninja, but also a bit more paranoid. For example, he might be more hesitant to trust new allies right away.
His relationships would change a lot. With Sasuke, he might be more of a distant observer rather than a passionate pursuer. With Sakura, he may not be as openly affectionate and more like a guiding figure. And with his other friends, he would probably keep a bit more distance, like Kakashi does, but still be there when they really need him.
He could become more protective. Since Kiva's powers are powerful, Naruto might feel a greater sense of responsibility to protect his village and friends. He might also be more secretive about his new powers, at least until he fully understands them. And his sense of humor might change a bit, becoming a bit darker or more sarcastic as he gets used to his new identity as someone with Kiva - like abilities.
Naruto's personality might still shine through even as an Arrancar. He's always been determined and kind - hearted. However, he could become a bit more solitary at first as he adjusts to his new form and powers. The Arrancar nature might make him more cautious in some ways, but his basic values of friendship and protecting the weak would remain. He might also develop a bit of an edge, as Arrancars are often seen as more menacing, but it would be a surface change. Deep down, he'd still be the Naruto who wants to bring peace and joy to his village.
If Naruto becomes a Jigsaw fan in fanfiction, his relationships would change drastically. His friends and comrades in Konoha would be confused and concerned. They have always known Naruto as a kind - hearted and positive person. His newfound interest in Jigsaw's ways would seem out of character. For instance, his bond with Hinata would be severely tested. Hinata, who loves Naruto for his heroic and gentle nature, would be at a loss on how to deal with this new, darker Naruto. His relationships with the other ninja clans in the village would also become tense as they would view his new ideology as a threat to the village's peace and stability.
With his gamer abilities, Naruto could attract new allies and enemies. Some might be drawn to his unique powers, seeing potential in teaming up with him. Others might view him as a threat. His relationship with the village as a whole could also change. If he becomes too powerful too quickly through his gamer abilities, some villagers might be scared, while others might see him as an even greater hero. This would all play out in complex ways in the fanfiction.
His relationship with Kurama might become more complex. Since he's now also a kitsune - like being. They could either become more competitive or find a new way to cooperate. With his friends, some might be in awe of his new form, while others might be a bit scared at first. But Naruto's kind heart would eventually make them all accept him as before.
If Naruto becomes a nukenin, his relationship with the village elders would be completely severed. They would see him as a threat, and he would see them as unjust. With his peers, some might side with him, believing in his innocence. Others would follow the village's orders out of loyalty. His bond with the Nine - Tails would also change. The Nine - Tails might offer more support, seeing Naruto as an outcast like itself.
His relationship with Sasuke would be greatly affected. Sasuke, who has his own experiences with the idea of killing, might see Naruto in a new light. They could either become rivals again or Sasuke might try to 'save' Naruto from his new dark path. With Sakura, she would be horrified. She's always seen Naruto as a positive force, and this change would make her question everything. She might even try to use her medical skills to 'cure' Naruto of his new - found killer tendencies.
If Naruto becomes a Saiyan in fanfiction, his relationship with his mentor, like Jiraiya, could be different. Jiraiya would have to guide Naruto in handling these new Saiyan powers. Naruto's friends might be both in awe and a little scared. For example, Sakura might be worried about Naruto losing control of his new powers. And his relationship with the villagers could change too. Some might see him as an even greater protector, while others might fear his new, more alien - like powers.